I should post up now that I've finally got this fixed.
I replaced the upper control board due to a switch that was nearly impossible to move to gas or electric. Still got the check light, although I could hear the fridge ignite, the light would come on after about 10 to 15 seconds.
During this time the trailer was plugged into my house and I was running the fridge on electric, and I found that it was freezing up. Following the guide I assumed the relay was bad and replaced the lower control board. The new board was supposed to help with check lights, but I still couldn't get the gas to stay lit.
I tested, then cleaned, the flame sensor and hooked it up. All seemed well, it ran on gas for several hours and didn't seem to be freezing in the fridge. I left it running on gas overnight, and the next morning the check light was back on and it again wouldn't stay lit.
Finally the only component left was the ignition control module, so I replaced it and found out that the new module doesn't use a flame sensor. It senses through the spark electrode. I had taken the trailer up to family property the weekend before Memorial, and installed the module up there. We stayed overnight and the fridge appeared to be working. We left only soda in the fridge and came back up on Memorial weekend, only to find the fridge still running, but everything frozen, and several of my wife's nasty Dr Peppers exploded all over the inside.
The next morning I removed the fridge and replaced the thermister with a Dometic unit by splicing my connector on. Nobody had one for a fridge this old. I got the fridge reinstalled, tested, and checked the propane line for leaks, and it worked perfectly. The next morning the fridge was cold, nothing frozen in the fridge, and it's been running great ever since (except the next weekend when the battery had died before we got there).
All told I spent about $400 on parts, and may not have needed the lower control board, but still worth replacing. The cost of a new 8 c.f. fridge is about $1400, so well worth my investment in time and money.